Determine how many solutions exist for the system of equations. ${-4x+y = -9}$ ${4x-2y = 20}$
Convert both equations to slope-intercept form: ${-4x+y = -9}$ $-4x{+4x} + y = -9{+4x}$ $y = -9+4x$ ${y = 4x-9}$ ${4x-2y = 20}$ $4x{-4x} - 2y = 20{-4x}$ $-2y = 20-4x$ $y = -10+2x$ ${y = 2x-10}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = 4x-9}$ ${y = 2x-10}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.